The whole point of having exchanges rather than simply trading over-the-counter is to have a paper trail of who owns what. If the exchange does not keep track of who owns what securities, then it's not doing its job. And tools that do not do their jobs should be replaced or discarded.

Of course, alphabet soup derivatives are typically traded over the counter rather than on exchange. But that's a bug, not a feature.

In Denmark, notes are notarised and placed in a similar sort of central registry as deeds and titles. But then again, in Denmark, everything is noted and registered and recorded in a central registry somewhere.

If a CDS were actually treated like an insurance policy, it would not be tradeable. The CDS could only be held by the buyer of a named beneficiary, and the payment obligation could be transferred only under highly regulated conditions. But then no one would score an endless series of commissions.